Comments for Size Comparison - How big would the earth be?

A direct proportion between two variables means that one variable is a constant multiple of the other variable.

The terms “proportional relationship”, “direct variation” and “direct proportion” all mean the same thing. The terms are interchangeable.

The equation for your question looks like this:

y = kx

k is a constant. It is called the “constant of variation”.

To solve for k:

y/x = k

The constant of variation means that DIVIDING the value of ONE VARIABLE BY THE value of the OTHER variable is a CONSTANT value (k, the constant of variation). (This can be applied to your problem).

The diameter of the earth divided by the diameter of the universe is a ratio (or proportion), a k value which I will name “k₁”.

The height of a human divided by the diameter of the universe is a different ratio, another k value which I will name “k₂”.

If I understand your question correctly, it is: if you scale the universe down to the size of an average human, what would the diameter of the earth be? In other words, you want to compute what the size of the earth would be using the ratio “k₁” (similar to you holding a grain of sand).

There is some difference of opinion as to what the diameter of the universe is. For the sake of argument, I am going to assume the universe is 93 billion light years in diameter.

Unfortunately the earth is not a perfect sphere. The diameter at the equator is slightly larger than the diameter between the north and south poles. I’m going to assume the diameter of the earth is 7,926 miles.

The average height of a human varies greatly. The average height of men and women is not the same, the average height varies by geographical location and race, and the average height varies by age. I’m going to arbitrarily assume the average height of a human is: 5 feet 9 inches. This is equivalent to 5.75 feet.

If the diameter of the universe is scaled down to the average height of a human, the diameter of the scaled down earth is:

8.3362817039202 ✕ 10-20 feet

This size is equivalent to 2.5408986633549*10-14 microns. This size is smaller than the diameter of a strand of spider web (2 – 3 microns), smaller than a particle of smoke (0.01 – 1 microns), and smaller than the diameter of an oxygen atom (0.0005 microns)